Flexible varieties and automorphism groups

Given an affine algebraic variety X of dimension at least 2, we let SAut (X) denote the special automorphism group of X i.e., the subgroup of the full automorphism group Aut (X) generated by all one-parameter unipotent subgroups. We show that if SAut (X) is transitive on the smooth locus of X then it is infinitely transitive on this locus. In turn, the transitivity is equivalent to the flexibility of X. The latter means that for every smooth point x of X the tangent space at x is spanned by the velocity vectors of one-parameter unipotent subgroups of Aut (X). We provide also different variations and applications.Comment: Final version; to appear in Duke Math.

Del Pezzo surfaces and local inequalities

I prove new local inequality for divisors on smooth surfaces, describe its applications, and compare it to a similar local inequality that is already known by experts.Comment: 13 pages; to appear in the proceedings of the conference "Groups of Automorphisms in Birational and Affine Geometry", Levico Terme (Trento), 201

Cremona groups of real surfaces

We give an explicit set of generators for various natural subgroups of the real Cremona group BirR(P2). This completes and unifies former results by several authors

A refined stable restriction theorem for vector bundles on quadric threefolds

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a closed subset of codimension at least 2 of the dual projective 4-space, and we explicitly describe the bundles E which do not enjoy this property. This refines a restriction theorem of Ein and Sols [Nagoya Math. J. 96, 11-22 (1984)] in the same way the main result of Coanda [J. reine angew. Math. 428, 97-110 (1992)] refines the restriction theorem of Barth [Math. Ann. 226, 125-150 (1977)].Comment: Ann. Mat. Pura Appl. 201

Machine learning denoising of high-resolution X-ray nanotomography data

High-resolution X-ray nano­tomography is a quantitative tool for investigating specimens from a wide range of research areas. However, the quality of the reconstructed tomogram is often obscured by noise and therefore not suitable for automatic segmentation. Filtering methods are often required for a detailed quantitative analysis. However, most filters induce blurring in the reconstructed tomograms. Here, machine learning (ML) techniques offer a powerful alternative to conventional filtering methods. In this article, we verify that a self-supervised denoising ML technique can be used in a very efficient way for eliminating noise from nano­tomography data. The technique presented is applied to high-resolution nano­tomography data and compared to conventional filters, such as a median filter and a nonlocal means filter, optimized for tomographic data sets. The ML approach proves to be a very powerful tool that outperforms conventional filters by eliminating noise without blurring relevant structural features, thus enabling efficient quantitative analysis in different scientific fields

A simply connected surface of general type with p_g=0 and K^2=2

In this paper we construct a simply connected, minimal, complex surface of general type with p_g=0 and K^2=2 using a rational blow-down surgery and Q-Gorenstein smoothing theory.Comment: 19 pages, 6 figures. To appear in Inventiones Mathematica

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

Short range ballistic motion in fluid lipid bilayers studied by quasi-elastic neutron scattering

Diffusion is the primary mechanism for the movement of lipids and proteins in a biological membrane. It is important in the formation of various macromolecular structures, such as lipid rafts. The commonly accepted theory for diffusion in membranes suggests that the molecules undergo continuous Brownian diffusion at long length scales, with a "rattling-in-the-cage" motion at short length scales, as shown in figure 1. However, this model has recently been challenged by experimental and simulation results. It has been observed that lipids move in loosely bound clusters rather than as individual molecules [1,2], and that there is a flow-like component to long range lipid diffusion [3]. Ballistic and sub-diffusive regimes have been observed in molecular dynamics simulations [4,5]. Diffusion is mainly studied by two experimental methods: fluorescence techniques and incoherent quasi-elastic neutron scattering. The two techniques access distinctly different length scales, resulting in a "blind spot" at mesoscopic distances. We note that the diffusion coefficients measured by these two techniques often differ by as much as orders of magnitude. The mechanism for diffusion, therefore, seems to depend on the length scale at which it is observed. The blind spot in the mesoscopic range will hopefully be closed in the future using high energy resolution lamor precession techniques performed with spin-echo spectrometers. To extend the window of length scales and investigate the motion of lipid molecules at very short distances, we used the unique capabilities of the IN13 thermal backscattering spectrometer. IN13 provides access to an exceptionally large Q range, covering length scales from 1.3 to 31 Å (0.2 Å -1 < Q < 5 Å -1 ). We used IN13 to study lipid diffusion at length scales smaller than a typical lipid-lipid distance in fluid bilayers. The aim of the experiment was to prove the validity of the Brownian diffusion model down to very small length scales. We chose a stacked model membrane system (DMPC) for this study and analysed the quasi-elastic neutron scattering response of the lipid molecules. Membranes were prepared as solid-supported, multi-lamellar membrane stacks on silicon wafers. Protonated lipids were hydrated by heavy water, so that the experiments were sensitive to the incoherent signal of the lipids. To increase the scattering signal, several wafers with thousands of highly oriented membranes were stacked. The membranes were studied in their physiologically relevant fluid state, at high temperature (T=30 °C) and full hydration. The width of the quasi-elastic energy response (full width at half maximum, FWHM) is shown in figure 2. If a particle diffuses via random Brownian motion, the time evolution of its displacement can be written as = 2Dt, and the quasi-elastic energy broadening has a Lorentzian shape, which demonstrate

Pushing the temporal resolution in absorption and Zernike phase contrast nanotomography: Enabling fast in situ experiments

Hard X-ray nanotomography enables 3D investigations of a wide range of samples with high resolution (<100 nm) with both synchrotron-based and laboratory-based setups. However, the advantage of synchrotron-based setups is the high flux, enabling time resolution, which cannot be achieved at laboratory sources. Here, the nanotomography setup at the imaging beamline P05 at PETRA III is presented, which offers high time resolution not only in absorption but for the first time also in Zernike phase contrast. Two test samples are used to evaluate the image quality in both contrast modalities based on the quantitative analysis of contrast-to-noise ratio (CNR) and spatial resolution. High-quality scans can be recorded in 15 min and fast scans down to 3 min are also possible without significant loss of image quality. At scan times well below 3 min, the CNR values decrease significantly and classical image-filtering techniques reach their limitation. A machine-learning approach shows promising results, enabling acquisition of a full tomography in only 6 s. Overall, the transmission X-ray microscopy instrument offers high temporal resolution in absorption and Zernike phase contrast, enabling in situ experiments at the beamline

The impacts of environmental warming on Odonata: a review

Climate change brings with it unprecedented rates of increase in environmental temperature, which will have major consequences for the earth's flora and fauna. The Odonata represent a taxon that has many strong links to this abiotic factor due to its tropical evolutionary history and adaptations to temperate climates. Temperature is known to affect odonate physiology including life-history traits such as developmental rate, phenology and seasonal regulation as well as immune function and the production of pigment for thermoregulation. A range of behaviours are likely to be affected which will, in turn, influence other parts of the aquatic ecosystem, primarily through trophic interactions. Temperature may influence changes in geographical distributions, through a shifting of species' fundamental niches, changes in the distribution of suitable habitat and variation in the dispersal ability of species. Finally, such a rapid change in the environment results in a strong selective pressure towards adaptation to cope and the inevitable loss of some populations and, potentially, species. Where data are lacking for odonates, studies on other invertebrate groups will be considered. Finally, directions for research are suggested, particularly laboratory studies that investigate underlying causes of climate-driven macroecological patterns